Abstract
The paper is the first of the series of two which analyses the h-p version of the finite element method in two dimensions. It proves the basic approximation results which in part 2 will be generalized and applied in a computational setting. The main result is that the h-p version leads to an exponential rate of convergence when solving problems with piecewise analytic data.
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References
Babuška, I.; Aziz, A.K. (1972): Survey lectures on the mathematical foundations of the finite element method. In: Aziz, A.K. (ed): The mathematical foundations of the finite element method with applications to partial differential equations, pp. 3–359. New York: Academic Press
Babuška, I.; Aziz, A.K. (1976): On the angle condition in the finite element method. SIAM J. Numer. Anal. 13, 214–226
Babuška, I.; Dorr, M.R. (1981): Error estimates for the combined h and p version of finite element method. Numer. Math. 37, 252–277
Babuška, I.; Gut, W.; Guo, B.; Szabo, B. (1986): Theory and performance of the h-p versions of the finite element method. (To appear)
Babuška, I.; Kellogg, R.B.; Pitkaranta, J. (1979): Direct and inverse error estimates with mesh refinement. Numer. Math. 33, 447–471
Babuška, I. ; Suri, M. (1986) : The optimal convergence rate of the p-version of the finite element method. (To appear)
Babuška, I.; Szabo, B.A.; Katz, I.N. (1981): The p-version of the finite element method. SIAM J. Numer. Anal. 18, 515–545
Bergh, I.; Lofstrom, J. (1976): Interpolation spaces. New York Berlin Heidelberg: Springer
Ciarlet, P.G. (1978): The finite element method for elliptic problems. Amsterdam: North-Holland
Dorr, M.R. (1985): The approximation theory for the p-version of the finite element method. SIAM J. Numer. Anal. 21, 1180–1207
Dorr, M.R. (1986): The approximation theory for the p-version of the finite element method. SIAM J, Numer. Anal. (In print)
Geldfand, I.M.; Shilov, G.E. (1964): Generalized functions, vol. 2. New York: Academic Press
Gui, W.; Babuška, I. (1985): The h, p and h-p versions of the finite element method of one dimensional problem. Part 1: The error analysis of the p-version, Tech. Note BN-1036. Part 2 : The error analysis of the h and h-p versions, Tech. Note BN-1037. Part 3 : The adaptive h-p version, Tech. Note BN-1038. Institute for Physical Science and Technology, University of Maryland, College Park
Guo, B.; Babuška, I. (1986) : Regularity of the solution of elliptic equations with piecewise analytic data. (To appear)
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Communicated by S.N. Atluri, August 4, 1985
Supported by the NSF Grant DMS-8315216
Partially supported by ONR Contract N00014-85-K-0169
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Guo, B., Babuška, I. The h-p version of the finite element method. Computational Mechanics 1, 21–41 (1986). https://doi.org/10.1007/BF00298636
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DOI: https://doi.org/10.1007/BF00298636